#### Math - 2019-20

# 7.8 - Probability

7.8The student willa)

determinethe theoretical and experimental probabilities of an event; andb)

investigateanddescribethe difference between the experimental probability and theoretical probability of an event.

*Adopted: 2016*

### BIG IDEAS

- I can predict my chances of winning a raffle, determine the
Heisman trophy winner, and foretell what flavor gumball will come out of the
machine next.

- I will understand that the likelihood of an event occurring can be described numerically and used to make predictions.

### UNDERSTANDING THE STANDARD

· In general, if all outcomes of an event are equally likely, the probability of an event occurring is equal to the ratio of desired outcomes to the total number of possible outcomes in the sample space.

· The probability of an event occurring can be represented as a ratio or equivalent fraction, decimal, or percent.

· The probability of an event occurring is a ratio between 0 and 1.

- A probability of 0 means the event will never occur.

- A probability of 1 means the event will always occur.

· The theoretical probability of an event is the expected probability and can be determined with a ratio.

· If all outcomes of an event are equally likely, the theoretical probability of an event =

· The experimental probability of an event is determined by carrying out a simulation or an experiment.

· The experimental probability of an event =

· In experimental probability, as the number of trials increases, the experimental probability gets closer to the theoretical probability (Law of Large Numbers).

### ESSENTIALS

- What is the difference between the theoretical
and experimental probability of an event?

Theoretical probability of an event is the expected probability and can be found with a formula. The experimental probability of an event is determined by carrying out a simulation or an experiment. In experimental probability, as the number of trials increases, the experimental probability gets closer to the theoretical probability.

**The student will use problem solving, mathematical
communication, mathematical reasoning, connections, and representations to**

·
7.8a_{1} **Determine**
the theoretical probability of an event.

·
7.8a_{2} **Determine**
the experimental probability of an event.

·
7.8b_{1} **Describe**
changes in the experimental probability as the number of trials increases.

·
7.8b_{2} **Investigate**
and **describe** the difference between
the probability of an event found through experiment or simulation versus the
theoretical probability of that same event.

### KEY VOCABULARY

experimental probability, theoretical probability, event, favorable
outcome, possible outcomes, experiment, trials, simulation, expected outcome,
Law of Large Numbers, difference

*Updated: Jul 30, 2019*